Continual Reasoning Gym: Diagnosing and Harnessing Shared Reasoning in Continual RLVR

Reinforcement learning with verifiable rewards (RLVR) commonly post-trains reasoning models on multiple tasks, while rerunning multitask RLVR (MTRL) as new tasks are added makes capability expansion costly. We therefore study continual RLVR, which updates the existing model as each task arrives. The central question is whether a model updated this way can perform as well as a jointly trained model. To answer this question, we introduce Continual Reasoning Gym, a continual-RLVR environment that organizes text and visual reasoning tasks into five task sequences. In this setting, we identify two key observations: Sequential RLVR exhibits modest forgetting, yet its final performance remains below that of MTRL. To understand the latter, we decompose final performance and show that forgetting accounts for only part of the gap. To explain the former, we identify shared reasoning: transferable reasoning structure allows training on one task to support others on average. We therefore introduce Continual Prompt Replay (CPR), which harnesses shared reasoning to improve learning on the arriving and future tasks by replaying previous-task prompts and regenerating their responses with the current policy. On average, only CPR reaches MTRL-level performance.

ComboShoppingBench: Evaluating LLM Agents for Budget-Constrained Basket Shopping with Coupons

Real-world shopping often requires constructing a basket of complementary items rather than retrieving a single product. Such combo-shopping tasks arise in device setup, meal preparation, event planning, and group takeout ordering, requiring joint reasoning about item compatibility, availability, store-level requirements, delivery fees, coupons, and budgets. Evaluation is challenging because multiple baskets may satisfy the same request, making exact-match metrics unsuitable, whereas semantic evaluation alone cannot detect infeasible orders, invalid coupon combinations, or incorrect payments. We introduce ComboShoppingBench, an agentic shopping benchmark for open-ended yet verifiable basket construction in a simulated commerce and takeout environment. During task synthesis, an exploration agent constructs a feasible and semantically coherent basket of purchasable products; this witness guides the generation of coupons, budget constraints, user queries, and aligned evaluation rubrics. During evaluation, LLM judges assess semantic satisfaction, response quality, and claim faithfulness, while deterministic validation checks product-ID validity, budget compliance, and coupon optimality. Experiments with diverse LLM agents demonstrate that even strong agents struggle on ComboShoppingBench, highlighting substantial room for improvement in reliable, constraint-aware combo shopping.

SPHERE: Mitigating the Loss of Spectral Plasticity in Mixture-of-Experts for Deep Reinforcement Learning

In deep reinforcement learning (DRL), an agent is trained from a stream of experience. In a continual learning setting, such agents can suffer from plasticity loss: their ability to learn new skills from new experiences diminishes over training. Recently, Mixture-of-Experts (MoE) networks have been reported to enable scaling laws and facilitate the learning of diverse skills. However, in continual reinforcement learning settings, their performance can degenerate as learning proceeds, indicating a loss of plasticity. To address this, building on Neural Tangent Kernel (NTK) theory, we formalize the plasticity loss in MoE policies as a loss of spectral plasticity. We then derive a tractable proxy for spectral plasticity, one expressible in terms of individual expert feature matrices. Leveraging this proxy, we introduce SPHERE, a practical Parseval penalty tailored for MoE-based policies that alleviates the loss of spectral plasticity. On MetaWorld and HumanoidBench, SPHERE improves average success under continual RL by 133% and 50% over an unregularized MoE baseline, while maintaining higher spectral plasticity throughout training.

MVR: Multi-view Video Reward Shaping for Reinforcement Learning

Reward design is of great importance for solving complex tasks with reinforcement learning. Recent studies have explored using image-text similarity produced by vision-language models (VLMs) to augment rewards of a task with visual feedback. A common practice linearly adds VLM scores to task or success rewards without explicit shaping, potentially altering the optimal policy. Moreover, such approaches, often relying on single static images, struggle with tasks whose desired behavior involves complex, dynamic motions spanning multiple visually different states. Furthermore, single viewpoints can occlude critical aspects of an agent's behavior. To address these issues, this paper presents Multi-View Video Reward Shaping (MVR), a framework that models the relevance of states regarding the target task using videos captured from multiple viewpoints. MVR leverages video-text similarity from a frozen pre-trained VLM to learn a state relevance function that mitigates the bias towards specific static poses inherent in image-based methods. Additionally, we introduce a state-dependent reward shaping formulation that integrates task-specific rewards and VLM-based guidance, automatically reducing the influence of VLM guidance once the desired motion pattern is achieved. We confirm the efficacy of the proposed framework with extensive experiments on challenging humanoid locomotion tasks from HumanoidBench and manipulation tasks from MetaWorld, verifying the design choices through ablation studies.

INSIGHT: End-to-End Neuro-Symbolic Visual Reinforcement Learning with Language Explanations

Neuro-symbolic reinforcement learning (NS-RL) has emerged as a promising paradigm for explainable decision-making, characterized by the interpretability of symbolic policies. For tasks with visual observations, NS-RL entails structured representations for states, but previous algorithms are unable to refine the structured states with reward signals due to a lack of efficiency. Accessibility is also an issue, as extensive domain knowledge is required to interpret current symbolic policies. In this paper, we present a framework that is capable of learning structured states and symbolic policies simultaneously, whose key idea is to overcome the efficiency bottleneck by distilling vision foundation models into a scalable perception module. Moreover, we design a pipeline that uses large language models to generate concise and readable language explanations for policies and decisions. In experiments on nine Atari tasks, our approach demonstrates substantial performance gains over existing NSRL methods. We also showcase explanations for policies and decisions.